The interest generated in Pauls savings account is $4.68
The amount generated in Larissa's savings account is $5015.80
What is Compound Interest ?Compound interest is interest that builds up over a certain length of time on both principal and interest. The principle is also used to account for the interest that has accrued on a principal over time. Furthermore, the cumulative principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over various time periods, the power of compounding is clearly apparent.
The interest that is paid on both principle and interest and is compounded on a regular basis is known as compound interest. The interest is calculated for the new principal at regular intervals when the accumulated interest and the current principal are combined. The initial principal plus the interest that has already accrued make up the new principal.
The initial principal(p) of Paul is $1000
rate(r) is 5.5%
Number of days(t) = 20th March to 20th April = 31 days = 31/365 years
So the Amount generated =[tex]p * (1 + \frac{r}{365})\x^{365*t}[/tex]
⇒ A = [tex]1000* (1 + \frac{5.5}{100*365})\x^{31} = 1000*1.00468 = 1004.68[/tex]
The interest generated = 1004.68 - 1000 = $4.68
Similarly for Larissa
time = 24th Feb to 17th March = 21 days = 21/365 years
So the Amount generated =[tex]p * (1 + \frac{r}{365})\x^{365*t}[/tex]
⇒ A = [tex]5000* (1 + \frac{5.5}{100*365})\x^{21} = 5000*1.00317 = 5015.80[/tex]
The amount generated is $5015.80
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a rectangle has its upper two vertices on the graph of and its lower two vertices on the -axis. what is the maximum possible area of the rectangle?
The maximum area of the rectangle is determined by the distance between the two points on the graph and the -axis.
What is rectangle?A rectangle is a four-sided shape with four right angles and two pairs of parallel sides. It is one of the most common shapes in the world, found in everything from building designs to artwork. Rectangles are also used in math, specifically to measure area and perimeter. Rectangles can also be classified according to their sides, with squares being a special type of rectangle with four equal sides.
To calculate the maximum possible area of the rectangle, we can use the formula A = (x2 - x1)(y2 - y1).
In this case, the two points on the graph have the same -coordinate, so the x2 - x1 part of the equation is zero. This means that the y2 - y1 part of the equation gives the maximum possible area of the rectangle. To calculate this, we need to take the difference between the two points on the graph.
For example, if the two points on the graph were (2,4) and (2,6), the maximum area of the rectangle would be (6 - 4) = 2.
Therefore, the maximum possible area of the rectangle is equal to the difference between the two points on the graph.
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Find at least three different sequences starting with 1. 2, 4 where the terms are generated by a simple rule.
Here are three different sequences starting with 1, 2, and 4, where the terms are generated by a simple rule:
1, 2, 4, 8, 16, 32, ...
The rule for this sequence is to multiply the previous term by 2.
1, 2, 4, 7, 11, 16, 22, ...
The rule for this sequence is to add the previous two terms.
1, 2, 4, 8, 14, 24, ...
The rule for this sequence is to multiply the previous term by 2 and then subtract it from the previous term.
Note that there is an infinite number of different sequences that can be generated by simple rules.
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A quare piece of cloth i ize 25 m quare i cut into rectangle trip of 50 50 cm wide find the number of tate and their total length in metre
All of the rectangles together measure 1250 meters in length.
A textile square with a 25 square meter surface area. We are aware that the area of a square is determined by multiplying one side's length by itself. The square root of 25 square meters, or 5 meters, is the length of one side of the square in this instance.
Secondly, we are aware that the fabric is being cut into 50 cm-wide rectangles. We can use the following formula to determine each rectangle's length:
(Rectangle width) x (Square cloth length) / (Width of square cloth)
The equation in this instance is (50 cm) x (25 m) / (5 m) = 2500 cm or 25 meters.
Therefore, each rectangle is 25 meters long.
We divide the square cloth's length by each rectangle's width to get the total number of rectangles.
25m / 0.5m (50cm) = 50 rectangles.
Finally, we multiply the quantity of rectangles by the average length of each rectangle to determine the total length of all the rectangles:
50 m x 25 m = 1250 m
Therefore, a square piece of fabric that is 25 square meters in size and has been divided into 50 rectangles, each measuring 50 cm wide and 25 meters long.
Therefore the rectangles together measure 1250 meters in length.
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After\ flying\ at\ an\ altitude\ of\ 600\ meters,\ a\ hot\ air\ balloon\ starts\ to\ descend.\ its\ g\operatorname{round}\ \operatorname{distance}\ from\ the\ landing\ pad\ is\ 10,000\ meters.\ What\ is\ the\ angle\ of\ depression,\ in\ degrees,\ \operatorname{for}\ this\ part\ of\ the\ flight\
Using the tangent side from trigonometric ratio, the angle of depression is 86.6 degrees
What is Angle of DepressionThe angle created between the line of sight to a location below the horizontal line and the horizontal line of sight is known as the angle of depression.
The angle of depression that the balloon makes with the launch pad can be calculated using the trigonometric ratio.
Data;
Opposite = 10000madjacent = 600angle = ?Since we have the opposite and adjacent side, we can use the tangent of the angle to find the angle of depression.
tanθ = opposite / adjacent
substituting the values into the formula
tan θ = 10000 / 600
tan θ = 100 / 6
tan θ = 16.666
θ = tan⁻¹(16.666)
θ = 86.6°
The angle of depression is 86.6°
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Given the linear system:
5x + 3y = 17
-8x - 3y = 9
What is the correct formula for the solution to the linear system?
The solution to the linear system is [tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} ,\ y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
A linear system of equation:
Ax + By = C
Dx + Ey = F
Can be solved using:
[tex]x=\frac{\left[\begin{array}{cc}C&B\\F&E\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}A&C\\D&F\end{array}\right]}{\left[\begin{array}{cc}A&B\\D&E\end{array}\right]}[/tex]
Hence, for:
5x + 3y = 17
-8x - 3y = 9
[tex]x=\frac{\left[\begin{array}{cc}17&3\\9&-3\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]} \\\\\\y=\frac{\left[\begin{array}{cc}5&17\\-8&9\end{array}\right]}{\left[\begin{array}{cc}5&3\\-8&-3\end{array}\right]}[/tex]
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Answer:
C
Step-by-step explanation:
Which statement is the best interpretation of the value 29,864 in the quadratic regression equation?
The company has an initial loss of about $29,864.
The company has an initial profit of about $29,864.
The company needs to sell about 29,864 units to break even.
The company needs to sell about 29,864 units to maximize its profit.
The interpretation of the value, 29,864, in the quadratic regression equation is the initial loss incurred by the company. The correct option is therefore;
The company has an initial loss of about $29,864What is a quadratic regression equation?A quadratic regression equation is the equation of the parabola that corresponds of best fits the points of the dataset on the coordinate plane.
The points on the graph of the question, obtained from a similar question, posted online are;
Number of units [tex]{}[/tex] Profits ($)
500 [tex]{}[/tex] -10000
1200 [tex]{}[/tex] 3000
2500 [tex]{}[/tex] 27000
3200 [tex]{}[/tex] 40000
3600 [tex]{}[/tex] 45000
4300 [tex]{}[/tex] 47000
5000 [tex]{}[/tex] 45000
6750 [tex]{}[/tex] 20000
The polynomial regression equation that corresponds to the points in the above table, obtained with MS Excel is presented as follows;
y = -0.004·x² + 34.637·x - 29864
Where;
y = The profit made
x = Number of units
When the company produces 0 units, x = 0, we get;
y = -0.004 × 0² + 34.637 × 0 - 29864 = -29864The 29864 is therefore the loss of $29864, of the company when the company produces zero units.
The correct option is therefore;
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A study selected independent random samples of 50 dogs and 60 cats and found that 38 of the dogs and 15 of the cats could be trained to fetch a ball. Do these data provide convincing evidence that the proportion of all dogs that can be trained to fetch a ball is greater than the proportion of all cats that can be trained to fetch a ball
On solving the provided question, we can say that 10% condition is met,
There are two separate random samples available.
what is random sample?selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.
There are two separate random samples available.
The 10% requirement is satisfied.
For both samples, 24, 26, 29, and 31 triumphs and failures are anticipated.
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I choose a random integer n between 1 and 10 inclusive. What is the probability that for the n I chose, there exist no real solutions to the equation x(x+5)=−n? Express your answer as a common fractio
The probability is 1/10.
The equation x(x+5) = -n can be rewritten as x^2 + 5x + n = 0. To find the solutions of this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 5, and c = n.
For there to be no real solutions, the discriminant (b^2 - 4ac) must be negative. The discriminant is 5^2 - 4(1)(n) = 25 - 4n. So for there to be no real solutions, 25 - 4n < 0, or n > 6.25.
Since the integer n is between 1 and 10 inclusive, the only value that would not have a real solution is n = 7. Therefore, the probability that for the randomly chosen n there exist no real solutions is 1/10.
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claire jogs $6$ miles per hour and megan jogs $5$ miles per hour. they start together at their campsite and jog to an outpost $18$ miles away. when claire gets there, she immediately turns around and heads back towards megan. how many miles will they be from the outpost when they meet? express your answer as a mixed number.claire jogs $6$ miles per hour and megan jogs $5$ miles per hour. they start together at their campsite and jog to an outpost $18$ miles away. when claire gets there, she immediately turns around and heads back towards megan. how many miles will they be from the outpost when they meet? express your answer as a mixed number.
When Claire and Megan meet, they will be $13\frac{1}{2}$ miles away from the outpost.
What is speed?Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.
This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone $9$ miles, and Megan will have gone $8\frac{1}{2}$ miles. When they meet, they will have gone a total of $17\frac{1}{2}$ miles, leaving them $13\frac{1}{2}$ miles away from the outpost.
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When Claire and Megan meet, they will be [tex]13\frac{1}{2}[/tex] miles away from the outpost. This can be solved by applying the concept of speed.
What is speed?Speed is the rate at which an object moves or travels over a period of time. It is measured in units such as meters per second (m/s) or kilometers per hour (km/h). Speed is a scalar quantity, meaning it has only magnitude and not direction. For example, a car travelling at 30 km/h has a speed of 30 km/h regardless of the direction it is travelling.
This is because Claire runs at a faster speed than Megan and will reach the outpost first. When she turns around and runs back, she will have gone 9 miles, and Megan will have gone [tex]8\frac{1}{2}[/tex] miles. When they meet, they will have gone a total of [tex]17\frac{1}{2}[/tex] miles, leaving them [tex]13\frac{1}{2}[/tex]miles away from the outpost.
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In the isosceles triangle has an interior angle measuring 134 degrees, what is the measure of each of the other two?.
Answer:
23°Step-by-step explanation:
In the isosceles triangle has an interior angle measuring 134 degrees, what is the measure of each of the other two?.the sum of the interior angles in a triangle is 180°, take away the know angle and divide by 2, it's an isosceles triangle so 2 side and 2 equal angles
(180 - 134) : 2 = (remember PEMDAS)
46 : 2 =
23°
----------------------------
check23 + 23 + 134 = 180°
the answer is goodthe hawks won 65% of their 60 games this year . how many games did they win ?
Answer: 24 games
Step-by-step explanation: 60-60%=24
HELP can all regular polygons fit in a larger polygon?
The property of square depicted is not common for all regular polygon
What is a regular polygon?If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.
The property showed how the square was merged with every two sides fully overlapping to form a bigger square
The trapezium which can also be a regular polygon (quadrilateral) lacks such property of arranging four trapeziums side by side, making overlaps that will form a bigger trapezium.
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The double number line shows that Jéssica lives 48 km from the capitol. 0 Distance (km) H Percentage 0% Distance (km) 48 12 60 48 Percentage Complete the table to show different percentages of the distance. + + 100% 1% of 48 km % of 48 km % of 48 km
The different percentages of the distance is 100%, 25% & 125%.
How to find the table to show different percentage of the distance?The Latin word "per centum," which means "by the hundred," served as the basis for the English word "percentage." Percentages are fractions with the denominator 100. In other words, it is the relationship between a part and a whole in which the value of the whole is always assumed to be 100.
A percentage is a fraction or ratio in which the whole value is always 100. For instance, Sam would have received 30 out of a possible 100 points if he had received 30% on his math test. It is expressed as 30/100 in fractional form and 30:100 in ratio form.
48 = 100% of 48
12 = 25% of 48
60 = 125% of 48
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a right rectangular prism 3 in by 4.25 in by 18.25 in what is the total surface area of the prism
The total surface area of the prism will be 290.125 Square units.
What is a surface area of a rectangular prism?The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.
The surface area of a rectangular prism is given by:
SA = 2 (lh +wh + lw )
where
l = 3
w = 4.25
h = 18.25
SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)
SA = 2 (54.75 + 77.5625 + 12.75)
SA = 2 (146.0625)
SA = 290.125 square units
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Solve for X, Leave in simplest radical form
Answer: X = [tex]\frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation: Because the two angles are equal (You circled them, also 45 degs), and there is a right triangle, which means that the 90-degree angle's adjacent sides are equal, in this case, both sides equal to X.
Using the special triangle ratio ( 1, 1, [tex]\sqrt{2}[/tex]), in this case, the "2" is equal to [tex]\sqrt{2}[/tex] times [tex]\sqrt{2}[/tex], so you have to divide the "1" (X) by [tex]\sqrt{2}[/tex], you simply get [tex]\frac{1}{\sqrt{2} }[/tex].
Sorry for my bad english
Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase (y) for different number of tickets (x) in the table shown. Do not add any spaces when typing in the equation.
The equation that models this linear function is y = 12.5x + 7.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept.Next, we would determine the slope of the data points in this table as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (44.50 - 32.00)/(3 - 2)
Slope, m = 12.5/1
Slope, m = 12.5.
At point (2, 32.00), a linear equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - 32.00 = 12.5(x - 2)
y - 32.00 = 12.5x - 25
y = 12.5x - 25 + 32.00
y = 12.5x + 7
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Complete Question:
Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase (y) for different number of tickets (x) in the table shown. What is the equation that models this linear function?
g eight children are divided into two teams each containing 4 children to play a game against each other. how many different divisions are possible?
70 different divisions are possible when eight children are divided into two teams each containing 4 children to play a game against each other
so this is what's known as a combination. a combination is a group where the order does not matter. to solve a combination, you use this equation:
n! / (r! *(n-r)!)
n is the total number of objects being sorted (8)
r is the group you need to sort them into (4)
(i know it's 2 groups of 4 but if you solve this for 1 group, the other group is automatically made of the remaining kids)
definition of !:
a number with a ! means 1*2*3...*that number (so that number multiplied by every number smaller than it all the way to one)
so we put 8 and 4 in this equation:
8! / (4! *(8-4)!)
simplify:
8! / *(4! 4!)
multiply out:
(8*7*6*5*4*3*2*1) / (4*3*2*1 * 4*3*2*1)
and put that in your calculator
you will get 70 different divisions are possible
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how to do distributive law in factorization?
Answer: it’s lar and we can’t compete against each other
Step-by-step explanation:
concept check 1. another word for mean is . margin centric statistic average product 2. which measure of central tendency is affected by outliers? mean median both mean and median mean, median, and mode 3. when would you calculate an expected value? when you need to know the exact outcome of a future, unknown event when your data points occur on different dates when you only have one data point when your data points have various probabilities of occurring 4. what is the median of the following set of numbers: 4, 0, -3, 5, 1, 3, -2? 3 5 1.14 1 5. true or false: the mode is universally an accurate representation of data sets because it captures the number that occurs most often. true false
Answer:
Another word for the mean is "average".
Which measure of central tendency is affected by outliers? Mean.
When would you calculate an expected value? when your data points have various probabilities of occurring.
What is the median of the following set of numbers: 4, 0, -3, 5, 1, 3, -2? 3.
True or false: The mode is universally an accurate representation of data sets because it captures the number that occurs most often. False. Mode is not always an accurate representation of data sets and it may not exist in certain data sets.
Step-by-step explanation:
______ are measures of center that summarize a typical data point
in a data set.
A. Mean and median
B. Median and interquartile range
C. Mean and mean absolute deviation
D. Mean absolute deviation and interquartile range
a mathematical organization is producing a set of commemorative license plates. each plate contains a sequence of five characters chosen from the four letters in aime and the four digits in $2007$. no character may appear in a sequence more times than it appears among the four letters in aime or the four digits in $2007$. a set of plates in which each possible sequence appears exactly once contains $n$ license plates. find $\frac{n}{10}$.
On solving the provided question we can say that there are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.
what is a sequence?A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.
N/10 has a value of 372.
The letters can be selected from the words "AIME" or "2007."
The only number that can be repeated twice is 0; there are seven different characters that can be chosen.
There are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.
There are 2520 possible sequences if 0 appears 0 or 1 times in the sequence.
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Determine the reactions at the roller A and pin B.B. 4 m 450 N 600 NmA. 2 m 3 m
The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N. To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N).
Reaction at Roller A:
2 m * 900 N = 1800 N
Reaction at Pin B:
3 m * 450 N + 600 N = 2450 N
To calculate the reaction at Roller A, you need to multiply the length of the roller (2 m) by the load (900 N). This gives you 1800 N.
To calculate the reaction at Pin B, you need to multiply the length of the pin (3 m) by the load (450 N) and add the additional load (600 N). This gives you 2450 N.
The reaction at Roller A is 1800 N and the reaction at Pin B is 2450 N.
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Question
Points A , B , and C are three vertices of a rectangle. Plot the three points. Then find the coordinates of the fourth point, D , to complete the rectangle. Finally, write the equation of the line that passes through points B and D and forms a diagonal of the rectangle. �
(
−
2
,
3
)
,
�
(
4
,
3
)
,
�
(
4
,
−
1
)
A(−2,3),B(4,3),C(4,−1)
The fourth co-ordinate of the rectangle is D (-2, -1). The equation of the line that passes through the points B and D is 3y = 2x + 3.
The given points are:
A(−2,3), B(4,3), C(4,−1)
When we plot these points on the graph we can easily estimate the fourth point which will be equidistant from A as the point C is from B and from the point C as the point A is from B.
Therefore, the diagonal points are B(4, 3) and D(-2, -1).
The equation of the line between these two points is:
(y - y1) = ((y2 - y1)/(x2 - x1)) (x - x1)
(y - 3) = ((-1 -3)/(-2 - 4)) ( x - 4)
y - 3 = (2/3) (x - 4)
3y - 9 = 2x - 8
3y = 2x + 1
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Write the set using the descriptive method:
(5, 10, 15, 20, 25}
Answer: study dum ahh
Step-by-step explanation:
Which of the following r values indicates the strongest relationship between two variables? +0.45
-0.30
+0.03
-0.45
According to the given option +0.03 is the r values that indicates the strongest relationship between two variables. The option 3 is correct.
The strength of the association between two variables is gauged using correlation coefficients. Although there are other kinds of correlation coefficients, Pearson's is the most widely used. A correlation coefficient frequently used in linear regression is Pearson's correlation. Correlation coefficients typically lie in the range of -1.00 to +1.00.
The closest value to +1 (positive correlation) or -1 is taken into consideration as the strongest correlation, per the rule of correlation coefficients (negative correlation).
A high correlation coefficient means that one variable's value is directly correlated with another.
There is no relationship between the two variables if the correlation coefficient is zero.
A negative correlation coefficient shows an adverse relationship between the values of the two variables.
According to the given option +0.03 is the r values that indicates the strongest relationship between two variables.
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Hey, so as you can see I know what the slope is, but i can't figure out the y intercept. Could someone please help me? Thanks!
Answer: (0, -1/3)
Step-by-step explanation: The answer is: (0, -1/3)
y=mx+b
Slope being "m"
And the y intercept being "b"
I think it's (0, -1/3)
......
..
Is the function even, odd, or neither. Use the graph to answer the question
Answer:
A. Even
Step-by-step explanation:
Even Function
A function is "even" when:
[tex]f(x) = f(-x) \;for\; all\; x\\\\[/tex]
Stated in other terms, the function graph is symmetric about the vertical(y-axis). The right part of the function graph about the y-axis is a reflection of the left part of the function graph about the y-axis
Looking at the function graph, we see it is indeed symmetric about the y-axis
Hence an even function
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $1150. What was the rate charged per hour by each mechanic if the sum of the two rates was $95 per hour?
Answer: Let's call the hourly rate of the first mechanic "r1" and the hourly rate of the second mechanic "r2".
We know that the total time they worked is 20 hours + 5 hours = 25 hours.
We also know that the sum of their hourly rates is $95 per hour, so:
r1 + r2 = $95
We can use this information along with the total amount they charged, $1150, to find out how much each mechanic charged. We know that the total amount charged is the product of the number of hours worked and the hourly rate. So we can use the following equation:
(20 hours * r1) + (5 hours * r2) = $1150
Now we can substitute the equation r1 + r2 = $95 into the above equation and solve for r1:
(20 hours * r1) + (5 hours * (95 - r1)) = $1150
20r1 + 475 - 5r1 = 1150
15r1 = 675
r1 = $45/hour
To find out the hourly rate of the second mechanic, we can use the equation r1 + r2 = $95
r2 = $95 - r1
r2 = $95 - $45
r2 = $50/hour
So the first mechanic charges $45 per hour and the second mechanic charges $50 per hour.
Step-by-step explanation:
Find the stable distribution for the regular stochastic matrix. [0.5 0.2 0.5 0.8 ]
As per the given matrix, the stable distribution for the regular stochastic matrix is [tex]\begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.40 \\0.10\end{bmatrix}[/tex]
The term matrix is defined as a set of numbers arranged in rows and columns so as to form a rectangular array.
Here we have given that the matrix is written as
[tex]\begin{bmatrix}0.5 & 0.2 \\0.5 & 0.8\end{bmatrix}[/tex]
In order to find the stable distribution for the regular stochastic matrix, we must know what does it means in matrix.
The term stable distribution for the regular stochastic matrix in math is defined as a square matrix whose columns are probability vectors. And the probability vector is a numerical vector whose entries are real numbers between 0 and 1 whose sum is 1.
Here in order to find the solution, we have to equate the value with x and y and then we have to cross multiply the terms, then we get,
=> [tex]\begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.5\times0.8 \\0.2\times0.5\end{bmatrix}[/tex]
When we simplify this we get the solution as,
[tex]= > \begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.40 \\0.10\end{bmatrix}[/tex]
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find a cartesian equation for the curve and identify it. r = 7 cos(θ)
The cartesian equation for the curve r = 7 cos(θ) is [x -(7/2)]²+y² = 49/4, which is the equation of a circle.
Given r =7 cosθ
Multiplying throughout by ‘r’,
r² =7r cos θ --- (1)
Consider x² + y² = r² and put x = r cos θ --- (2)
x² + y² = 7x
Using completing the square method:
x² - 7x + (7/2)² + y² = (7/2)²
[x - (7/2)]² + y² = 49/4
(x - 7/2)² + (y - 0)² = (7/2)²
This is the equation of the circle with a center (7/2, 0) and radius of 7/2.
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